next up previous [pdf]

Next: Acknowledgments Up: Fomel & Grechka: Nonhyperbolic Previous: ANISOTROPY VERSUS LATERAL HETEROGENEITY

Conclusions

Nonhyperbolic reflection moveout of $P$-waves is sometimes considered as an important indicator of anisotropy. Its correct interpretation, however, is impossible without taking other factors into account. In this paper, we have considered three other important factors: vertical heterogeneity, curvature of the reflector, and lateral heterogeneity. Each of them can have an influence on nonhyperbolic behavior of the reflection moveout comparable to that of anisotropy. In particular, vertical heterogeneity produces a depth-variant anisotropic pattern that differs from that in VTI media. For isotropic media, this pattern is reasonably well approximated by the shifted hyperbola. In a vertically heterogeneous VTI medium, the parameters of anisotropy should be replaced with their effective values. For a curved reflector in a homogeneous VTI medium, we have developed an approximation based on the Taylor series expansion of the traveltime with both the reflector curvature and the anisotropic parameters entering the nonhyperbolic term. Lateral heterogeneity can effectively mimic the influence of virtually any anisotropy.

The theoretical results of this paper are directly applicable to modeling of the nonhyperbolic moveout. The general formulas connecting the derivatives of reflection traveltime with those of direct waves are particularly attractive in this context. For smooth velocity models, these formulas reduce the problem of tracing a family of reflected rays to tracing only one zero-offset ray. Practical estimation and inversion of nonhyperbolic moveout is a different and more difficult problem than is the forward one. Given that a variety of reasons might cause similar nonhyperbolic moveout of $P$-waves, its inversion will be nonunique. Nevertheless, the theoretical guidelines provided by the analytical theory are helpful for the correct formulation of the inverse problems. They explicitly show us which medium parameters we may hope to extract from the kinematics of long-spread $P$-wave reflection data.


next up previous [pdf]

Next: Acknowledgments Up: Fomel & Grechka: Nonhyperbolic Previous: ANISOTROPY VERSUS LATERAL HETEROGENEITY

2013-03-03